As a Seminole alumnus, I'm hopeful that FSU will fight the NCAA decision in court regardless of whether or not they win their appeal. In fact, I'm not sure they should even appeal at all, because by doing so, they may be legally acknowledging the NCAA's right to enact this ban and may lose standing to seek a remedy in court.
Assume FSU wins on appeal, which they surely will if they NCAA actually looks at the facts. Will it be acceptable to Seminole fans that the NCAA could, at any time, ban the FSU nickname and mascot again if the political conditions change? Say, if the Oklahoma Seminole Nation were to have a change of heart a couple of years from now and vote to condemn FSU's use of the mascot - would that be grounds for the NCAA to revisit the issue and ban FSU's mascot again? Giving the NCAA this power is unacceptable and must be fought to the highest level.
I think the court of public opinion is rising up to speak and be heard.
I always thought the NCAA was sort of the police department of college athletics, busting schools who cheated in recruiting football and basketball players and other shenanigans. I didn't realize they'd assumed authority as thought police as well. I'm no FSU fan, but I think you're right in saying they should take this to court, even if those PC clowns do back down.
If the NCAA is supposed to reign in out of control programs, somebody needs to reign them in, because this is the epitome of an out of control organization.